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This article is cited in 4 scientific papers (total in 4 papers)
New periodic Gibbs measures for $q$-state Potts model on a Cayley tree
Rustamjon M. Khakimov
Institute of Mathematics, National University of Uzbekistan,
Do’rmon Yo’li, 29, Tashkent, 100125, Uzbekistan
Abstract:
In this paper under some conditions on parameters of the $q$-state Potts model on a Cayley tree of order k we prove existence of the periodic (non translation-invariant) Gibbs measures. Also we give a result about the number of such measures.
Keywords:
Cayley tree, configuration, Potts model, Gibbs measure, periodic Gibbs measures, translation-invariant measures.
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UDC:
517.98
Received: 06.03.2014
Received in revised form: 29.04.2014
Accepted: 26.05.2014
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Citation:
Rustamjon M. Khakimov, “New periodic Gibbs measures for $q$-state Potts model on a Cayley tree”, J. Sib. Fed. Univ. Math. Phys., 7:3 (2014), 297–304
Citation in format AMSBIB
\Bibitem{Kha14}
\by Rustamjon~M.~Khakimov
\paper New periodic Gibbs measures for $q$-state Potts model on a Cayley tree
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2014
\vol 7
\issue 3
\pages 297--304
\mathnet{http://mi.mathnet.ru/jsfu374}
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http://mi.mathnet.ru/eng/jsfu374 http://mi.mathnet.ru/eng/jsfu/v7/i3/p297
Citing articles on Google Scholar:
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English articles
This publication is cited in the following articles:
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R. M. Khakimov, F. Kh. Khaidarov, “Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree”, Theoret. and Math. Phys., 189:2 (2016), 1651–1659
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F. Haydarov, R. Khakimov, “An improvement of extremality regions for Gibbs measures of the Potts model on a Cayley tree”, Algebra, Analysis and Quantum Probability, Journal of Physics Conference Series, 697, eds. S. Ayupov, V. Chilin, N. Ganikhodjaev, F. Mukhamedov, I. Rakhimov, IOP Publishing Ltd, 2016, 012019
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U. A. Rozikov, R. M. Khakimov, F. Kh. Khaidarov, “Extremality of the translation-invariant Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 196:1 (2018), 1043–1058
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R. M. Khakimov, M. T. Makhammadaliev, “Translation Invariance of the periodic Gibbs measures for the Potts model on the Cayley tree”, Theoret. and Math. Phys., 199:2 (2019), 726–735
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